Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

//import graph_representation.edge;
public class hacker49 {
	public static int r1=0;
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
	static HashMap<Long,Integer> e=new HashMap<>();
	public static void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();
	
		int n=s.nextInt();
		long[] a=new long[n+1];
		for(int i=1;i<=n;i++) {
			a[i]=s.nextLong();
		}
				Arrays.sort(a);
//			long[] b=new long[n+1];
				ArrayList<Long> e=new ArrayList<>();
				if(n%2==0) {
					int i=1;
					int j=n/2;
					while(i<=n/2-1) {
						e.add(a[j]);
						e.add(a[i]);
						i++;
						j++;
					}
					while(j<=n) {
						e.add(a[j]);
						j++;
						
					}
				}else {
					int i=1;
					int j=n/2+1;
					while(i<=n/2) {
						e.add(a[j]);
						e.add(a[i]);
						i++;
						j++;
					}
					while(j<=n) {
						e.add(a[j]);
						j++;
					}
					
				}
				int count=0;
				for(int k=1;k<e.size()-1;k++) {
					if(e.get(k)<e.get(k-1) && e.get(k)<e.get(k+1)) {
						count++;
					}
				}
			out.println(count);
			for(int k=0;k<n;k++) {
				out.print(e.get(k)+" ");
			}
	out.close();
	}
	static class pair5{
		private int a;
		private int b;
		pair5(int a,int b){
			this.a=a;
			this.b=b;
		}
	}
	static ArrayList<Integer>[] t=new ArrayList[200001];
	static int[] vis=new int[200001];
	static int g=0;
	static boolean p=true;
	static void dfs(int node,int par) {
		vis[node]=1;
		g++;
//		boolean p=true;
		if(t[node].size()>2) {
			p= false;
		}
//		boolean p=false;
		int c=0;
		for(int i=0;i<t[node].size();i++) {
			if(vis[t[node].get(i)]==0) {
				c++;
				  dfs(t[node].get(i),par);
			}
		}
		if(c==0) {
			if(!t[node].contains(par) || t[node].size()<2) {
				p= false;
			}
		}
//		return p;
	}
	static class pair implements Comparable<pair>{
		private long i;
		private long v;
		pair(long i,long v){
			this.i=i;
			this.v=v;
		}
		public int compareTo(pair o) {
//			if(o.v<this.v) {
//				return -1;
//			}else {
//				return 1;
//			}
			return Long.compare(this.v, o.v);
		}
		
	}
	
	static int nextPowerOf2(int n) 
	{ 
	    n--; 
	    n |= n >> 1; 
	    n |= n >> 2; 
	    n |= n >> 4; 
	    n |= n >> 8; 
	    n |= n >> 16; 
	    n++; 
	      
	    return n; 
	} 
//	static class node{
//		private int a;
//		private int b;
//		private int c;
//		private int d;
//		
//	}
	
	
	public static class node{
		private int a;
		private int b;
		node(int a,int b){
			this.a=a;
			this.b=b;
		}
	}

	public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
//	public static void Create(node[] arr,node[] segtree,int low,int high,int pos) {
//		if(low==high) {
//			segtree[pos]=arr[low];
//			return;
//		}
//		int mid=(low+high)/2;
//		Create(arr,segtree,low,mid,2*pos+1);
//		Create(arr,segtree,mid+1,high,2*pos+2);
//		if(segtree[2*pos+1].a+segtree[2*pos+2].a>=10) {
//			int a=segtree[2*pos+1].a;
//			int b=segtree[2*pos+2].a;
//			int c=segtree[2*pos+1].b;
//			int d=segtree[2*pos+2].b;
//			segtree[pos]=new node((a+b)%10,1+c+d);
//		}else {
//			int a=segtree[2*pos+1].a;
//			int b=segtree[2*pos+2].a;
//			int c=segtree[2*pos+1].b;
//			int d=segtree[2*pos+2].b;
//			segtree[pos]=new node(a+b,c+d);
//			
//		}
//	}
//	public static node Query(node[] segtree,int qlow,int qhigh,int low,int high,int pos) {
//		if(low>=qlow && high<=qhigh) {
//			return segtree[pos];
//		}
//		if(qhigh<low || qlow>high) {
//			return new node(0,0);
//		}
//		int mid=(low+high)/2;
//	 node a=Query(segtree,qlow,qhigh,low,mid,2*pos+1);
//	node b=Query(segtree,qlow,qhigh,mid+1,high,2*pos+2);
//	int c=a.a;
//	int d=b.a;
//	if(c+d>=10) {
//	node e=new node((c+d)%10,1+a.b+b.b);
//	return e;
//	}else {
//		node e=new node(c+d,a.b+b.b);
//		return e;
//	}
//	}
//	
	static class pair1 implements Comparable<pair1>{
		private int a;
		private int b;
		private int c;
		private int d;
		pair1(int a,int b,int c,int d){
			this.a=a;
			this.b=b;
			this.c=c;
			this.d=d;
		}
		public int compareTo(pair1 o) {
			if(this.a<o.a) {
				return 1;
			}else if(this.a==o.a) {
				if(this.b<o.b) {
					return 1;
				}else {
					return -1;
				}
			}else {
				return -1;
			}
				
		}
	}
	public static void update(long[] segtree,int low,int high,int qlow,int qhigh,long val,int pos) {
		if(qlow>high || qhigh<low) {
			return ;
		}
		if(low>=qlow &&qhigh>=high) {
			segtree[pos]+=val;
			return;
		}
		int mid=(low+high)/2;
		update(segtree,low,mid,qlow,qhigh,val,2*pos);
		update(segtree,mid+1,high,qlow,qhigh,val,2*pos+1);
		
	}
	public static long query(long[] segtree,int low,int high,int index,int pos) {
		
		if(low==high) {
			return segtree[pos];
		}
		int mid=(low+high)/2;
		long res=0;
		if(index<=mid) {
			res= query(segtree,low,mid,index,2*pos);
		}else {
			res=query(segtree,mid+1,high,index,2*pos+1);
		}
		return res+segtree[pos];
	}
	
//	public static class pair5{
//		private int a;
//		private int b;
//		pair5(int a,int b){
//			this.a=a;
//			this.b=b;
//		}
//		public int compareTo(pair5 o) {
//			return Integer.compare(o.b, this.b);
//		}
//	}
//	public static pair5[] merge_sort(pair5[] A, int start, int end) {
//		if (end > start) {
//			int mid = (end + start) / 2;
//			pair5[] v = merge_sort(A, start, mid);
//			pair5[] o = merge_sort(A, mid + 1, end);
//			return (merge(v, o));
//		} else {
//			pair5[] y = new pair5[1];
//			y[0] = A[start];
//			return y;
//		}
//	}
//	public static pair5[] merge(pair5 a[], pair5 b[]) {
////		int count=0;
//		pair5[] temp = new pair5[a.length + b.length];
//		int m = a.length;
//		int n = b.length;
//		int i = 0;
//		int j = 0;
//		int c = 0;
//		while (i < m && j < n) {
//			if (a[i].a < b[j].a) {
//				temp[c++] = a[i++];
//			} else {
//				temp[c++] = b[j++];
//			}
//		}
//		while (i < m) {
//			temp[c++] = a[i++];
//		}
//		while (j < n) {
//			temp[c++] = b[j++];
//		}
//		return temp;
//	}
////	
	public static int upper_bound(int[] a ,int n,int x) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return r;
				
	}

//	
//	
	public static int lower_bound(pair[] a ,int n,long x) {
		int l=0;
		int r=n+1;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid].i<x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;
				
	}
	public static int ty(int[] a, int x, int y)
    {
        Arrays.sort(a);
        int count=0;
        int n=a.length;
        for(int i=0;i<n;i++) {
        	int g=0;
        	if(x%a[i]==0) {
        		g=x/a[i];
        	}else {
        		g=x/a[i]+1;
        	}
        	int k1=upper_bound(a,n,g);
        	if(k1==n) {
        		count+=0;
        	}else {
        		int g1=0;
            	if(y%a[i]==0) {
            		g1=y/a[i];
            	}else {
            		g1=y/a[i]+1;
            	}
//            	int k2=lower_bound(a,n,g1);
//            	if(k2>=k1) {
//            		count+=(k2-k1+1);
//            	}
        	}
//        System.out.println(count);
        }
        return count;
        
    }
	static boolean isValid(int x,int y,int n,int m) {
		if(x>=1 && x<=n && y>=1 && y<=m) {
			return true;
		}else {
			return false;
		}
	}
	
	static long[] fac=new long[1000001];
	static void fac() {
		fac[0]=1;
		for(int i=1;i<=1000000;i++) {
//			fac[i]=((fac[i-1]%mod)*(i%mod))%mod;
		}
	}
	static ArrayList<Integer>[] f=new ArrayList[2001];
	public static void init(int n) {
		
		for(int j=1;j<=n;j++) {
		for (int l=1; l<=Math.sqrt(j); l++)
        {
            if (j%l==0)
            {
                // If divisors are equal, print only one
                if (j/l == l) {
                    f[j].add(l);}
      
                else { // Otherwise print both
//                    System.out.print(i+" " + n/i + " " );
            f[j].add(l);
            f[j].add(j/l);
                }
                
            }
        }
		
		}
		
	}
	
	public static long[] merge_sort(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort(A, start, mid);
			long[] o = merge_sort(A, mid + 1, end);
			return (merge(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge(long a[], long b[]) {
//		int count=0;
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}
	
	public static long[] merge_sort1(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort1(A, start, mid);
			long[] o = merge_sort1(A, mid + 1, end);
			return (merge1(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge1(long a[], long b[]) {
//		int count=0;
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}
	
	static long MOD=1000000007;
	static class pair2{
		private long a;
		private int b;
		pair2(long a,int b){
			this.a=a;
			this.b=b;
		}
	}
	




//	for(int i=2;i<=100000;i++) {
		
	
}